<i>SU</i>(3)×𝒮<sub>20</sub> algebras for uniform spin‐1 ensembles on [<sup>2</sup><i>H</i><sup>12</sup><i>C</i>]<sub>20</sub>, or [<sup>14</sup><i>N</i>]<sub>20</sub>, dodecahedrane‐type lattices and analogous isotopomeric [<i>M</i><sub>20</sub><sup>12</sup><i>C</i><sub>40</sub>] met‐carb subensembles: <i>M</i>‐based cardinalities and completeness of 𝒮<sub>20</sub> spin irreps, via hierarchical {𝒞<sup>λ⊢(<i>n</i>=20):(<i>M</i>)</sup>} designs of polyhedral combinatorics*
Bibliographic record
Abstract
Abstract The M ‐based hierarchy cardinalities of spin irreps for \documentclass{article}\pagestyle{empty}\begin{document}$[A]_{20}^{(I_{i}=1)}$\end{document} uniform nuclear magnetic resonance (NMR) /isotopomer spin ensembles are derived. Such ideas define the completeness of the number‐partition‐based (intermediate) combinatorial designs (on M) themselves inherent in specific λ⊢ n digit assembly combinatorial properties. Illustrative M ‐subspatial irrep subsets are derived via Schur decompositions from symbolic algorithms (Sagan, B. E. Symmetric Group: Representations, C‐Algorithms, Symmetric Functions; Wadsworth: Belmont, CA, 1991; SYMMETRICA package, as per Kerber, A.; Kohnert, A.; Lascoux, A. Symbolic Comput 1992, 14, 195). The results are discussed in the context of the independant cardinality of underlying system scalar invariants (SI) corresponding to the democratic auxiliary labels (Chem Phys 1998, 238, 245; J Math Chem in press), or projective recoupling, of 20‐fold dual tensorial sets. Landau‐like 𝒮 n ‐maps for fundamental terms plus statistical weighted subsidary maps yield the independent ∣ SI ∣s (see Europhys Lett in press). Geometric aspects of the dual group mappings imply that eventually large cage NMR ensembles must be governed by a local, rather than a global, symmetry, with the former related to established spectral deceptive NMR. This suggests a further role for dynamical networks in NMR, beyond that given by K. Balasubramanian (J Chem Phys 1983, 78, 6369) as implied by D. Watts (Small Worlds; Princeton Univ. Press: Princeton, NJ, 1999). © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.005 | 0.002 |
| Meta-epidemiology (narrow) | 0.007 | 0.007 |
| Meta-epidemiology (broad) | 0.009 | 0.005 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.007 | 0.002 |
| Research integrity | 0.004 | 0.007 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; both teacher heads agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".